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Imprecise computations allow scheduling algorithms developed for energy-constrained computing devices to trade off output quality with utilization of system resources. The goal of such scheduling algorithms is to utilize imprecise computations to find a feasible schedule for a given task graph while maximizing the quality of service (QoS) and satisfying a hard deadline and an energy bound. This work presents a heuristic for scheduling tasks with potentially imprecise computations, represented with directed acyclic graphs, on multiprocessor platforms. Furthermore, it presents a mixed integer linear program formulation of the same problem, which provides the optimal reference scheduling solutions, enabling evaluation of the efficacy of the proposed heuristic. Both the heuristic and mathematical program take account of potentially imprecise inputs of tasks on their output quality. Furthermore, the presented heuristic is capable of finding feasible schedules even under tight energy budgets. Through extensive experiments, it is shown that in some cases, the proposed heuristic is capable of finding the same QoS as the ones found by MILP. Furthermore, for those task graphs that MILP outperforms the proposed heuristic, QoS values obtained with the proposed heuristic are, on average, within 1.24% of the optimal solutions while improving the runtime by a factor of 100 or so. This clearly demonstrates the advantage of the proposed heuristic over the exact solution, especially for large task graphs where solving the mathematical problem is hampered by its lengthy runtime.

Energy-aware Scheduling of Task Graphs with Imprecise Computations and End-to-end Deadlines